>Conceptual experiment: Push your finger against a paper clip, deflecting it >1 mm. Easy. Let's call that amount of force (applied with your finger) F. >Now deflect it another mm. Still easy. That amount of force is actually >2*F. Now repeat this experiment, only this time assist your finger with an >enormous leaf spring from a diesel truck, which you will use to deflect the >paperclip by exactly 1 mm. The force now required from your finger to >deflect the paperclip that 1 mm (i.e. no more than it's already deflected) >is zero. Cool. Does that mean the new assembly has no more stiffness? No. >Try deflecting the assembly (the two springs in combination) that second mm. >Good luck. > >The conclusion: Spring constant (stiffness) is additive. Total spring >constant in the above example is that of the paperclip plus that of the leaf >spring. Neither element can contribute more than 100% of the total >stiffness, although the leaf spring certainly provides 99.999999% of it. Hi Sarah, Yes, I do understand both the principal and the logic. Run your conceptual experiment with a more representative set of springs. The rib isn't a truck spring. It's another paper clip. Clip#1 is the rib, pushing down, clip#2 is the panel compression levering the rib up. The spring rate of clip#2 is, indeed, slightly higher than #1, but not by tens of thousands. Now add a third clip. Clip#3 represents the string bearing. It is pushing in the same direction as clip#1. To maintain relative position, clip#2 (the panel) must balance the force of clips#1, and #3. That's compression crowned. In the rib crowned spring simulation (same cast of paper clip springs), both clip#1 (rib) and clip#2 (panel compression) are opposing clip#3 (bearing). I realize nothing can produce over 100% of what it can produce. The question I was answering about which (panel or rib) contributes more to the stiffness in a rib crowned, vs a panel crowned board. In that context, the panel in a panel crowned board contributes more than 100% of the spring resistance necessary to support string bearing because it has to lift the spring resistance of the rib as well. Ron N
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